a car is purchased for $25,000 and has a resale value of $19,000 after a useful life of 6 years. using a…
a car is purchased for $25,000 and has a resale value of $19,000 after a useful life of 6 years. using a book value depreciation chart, calculate the number of years until the book value of the car is $23,000.
Answer
Explanation:
Step1: Calculate annual depreciation
The car is purchased for $P = 25000$ and has a resale - value of $S=19000$ after $n = 6$ years. The total depreciation is $D=P - S=25000 - 19000 = 6000$. The annual depreciation $d$ is given by the formula $d=\frac{D}{n}$. So, $d=\frac{6000}{6}=1000$ per year.
Step2: Calculate the amount of depreciation to reach the target book - value
The initial value of the car is $25000$ and the target book - value is $23000$. The amount of depreciation $x$ to reach the target book - value is $x = 25000 - 23000=2000$.
Step3: Calculate the number of years
Since the annual depreciation is $1000$, and the total depreciation needed is $2000$, the number of years $y$ is given by $y=\frac{x}{d}$. Substituting $x = 2000$ and $d = 1000$, we get $y = 2$.
Answer:
2